Loop quantum f(R) theories

As modified gravity theories, the four-dimensional metric f(R) theories are cast into connection-dynamical formalism with real su(2) connections as configuration variables. This formalism enables us to extend the nonperturbative loop quantization scheme of general relativity to any metric f(R) theories. The quantum kinematical framework of f(R) gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for f(R) theories are well defined. Our results show that the nonperturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.